(1) Field of the Invention
The present invention is generally drawn to an automated design system for structures using a "Finite Element" database, which system has been particularly adapted to the design of offshore engineering structures. The database is controlled by IDMS, a general-purpose sophisticated database management control system.
(2) Description of the Prior Art
For many decades, the science of advanced stress analysis remained essentially stagnant. This was not due to a lack of theoretical understanding but because of the limitations of numerical computation. Thus, if the shape of the stressed workpiece or the system or applied load did not conform to a standard set of known solutions, the stress analyst had to then make it fit as best as he could by assuming some simplified shape or loading system that approximated the case at hand.
Nowadays, by using the Finite Element Method (FEM), stress analysts do not have to modify the problem to conform to available solutions. No matter how complex the shape or system of loads may be, the (FEM) treats a loaded structure as being built of numerous tiny connected substructures or elements as are shown in FIG. 8. Since these elements can be put together in virtually any fashion, they can be arranged in simulate exceedingly complex shapes. Thus, the (FEM) can be used to determine stresses for structural parts where no mathematically closed form solution exists.
The reliable accuracy of the (FEM) has rendered some of the most elegant experimental techniques, for example, two-dimensional photo-elasticity, obsolete. Another important aspect of the (FEM), for example, is that it is not limited to ordinary stress analysis. Non-linear material properties, plasticity and dynamics are all within the scope of the method. Furthermore, (FEM) can be applied to a broad class of problems called field problems, which include topics like electrical potential, heat flow, and nuclear fusion, to name but a few.
The idea of modelling complex structures as a collection of well-defined structural elements, such as BEAMS, PLANTS, and SHELLS, was put forward and received much attention. The (FEM), did not first appear until the 1960's. Computer systems available at that time did not provide the capacity required to model and solve practical design problems within the realistic time and cost restrictions of most production design schedules.
Most of the development activity centered not only on the generation of large-scale structural computer programs as NASTRAN, but also on the development of sophisticated numerical methods for solving large sets of linear simultaneous equations.
The second milestone in the development of the (FEM) occurred in the mid-sixties with the advent of third generation computers. For the first time the computer power required to solve complex engineering problems became available. Time-sharing computers, which allowed for more efficient interaction with the stress analyst, and faster solution of engineering design problems were also introduced.
In its simplest form the FEM process is done according to the following steps:
The structural part is divided into discrete "Finite Elements", selected from the available library of fully developed and tested elements as shown in FIG. 8.
These "Finite Elements" are assumed to be connected together at discrete points called Nodes. Each Node usually has 6 degrees of freedom for its possible displacements: 3 translations and 3 rotations.
The position of these Nodes in space is defined by specifying their coordinates relative to some reference point using a rectangular, cylindrical or spherical reference coordinate system.
For each "Finite Element" a matrix, called the B matrix, is constructed from its geometrical properties.
For each "Finite Element" another matrix, called the D matrix, is constructed from the elastic properties of the materials used.
For each "Finite Element", a stiffness matrix k, is constructed by applying simple mathematical transformations to both the B and D matrices; k is always symmetric and consists of n2 submatrices, where n is the number of Nodes in the "Finite Element". Furthermore, each submatrix in k is of order d, where d is the number of degrees of freedom of the relevant Node.
A global stiffness matrix K is then constructed using the individual matrices k, such that displacements are compatible at each common Node.
The loads applied to the structure are then represented by equivalent loads applied on the relevant Nodes of the Finite Element Model. This results in the set of simultaneous equations EQU Kr=R, (1)
where K is the global stiffness matrix, r is the displacement vector, and R is the load vector.
K is always symmetric, thus only it's upper or lower triangle need be stored or processed; it consists of N2 submatrices, where N is the total number of Nodes in the "Finite Element" Model. As with the "Finite Element" stiffness matrix k, each submatrix in K is of order d.
Some Nodes are usually constrained against movement, in order to support the loaded structure. To take account of this, the appropriate degrees of freedoms in the relevant Nodes are set to zero.
The above equations, i.e. (1), are then solved, giving the final displacements for all of the degrees of freedoms of the Nodes in the Model.
The state of strain, and hence the state of stress, in each "Finite Element" is then fully obtained from the displacements of each "Finite Element".
The global stiffness matrix K may refer to more degrees of freedom than is required for the problem in hand. In this case, a technique called static condensation can be used to condense K by eliminating the unwanted degrees of freedom; these are usually called internal or dependent degrees of freedom.
The resulting condensed or reduced stiffness matrix, K', expresses the stiffness of the structure in terms of the reduced number of degrees of freedom chosen; these are usually referred to as external, boundary or independent degrees of freedom. Thus, static condensation is essentially a process of partial elimination of the unknown internal displacements. The resulting reduced stiffness equations may be written as EQU K'r'=R', (2)
where K' is the reduced stiffness matrix, r' is the reduced displacement vector, and R' is the reduced load vector. Static condensation is essentially the process of computing K' and R', as follows:
Assemble the stiffness equations.
Partition the coefficient matrix of these equations into dependent and independent submatrices corresponding to the set of dependent and independent degrees of freedom.
Compute K'. This process usually involves a matrix inversion (or equivalent), which, for large problems, may require considerable computer resources.
By way of example, the simply-supported, loaded, continuous beam, as shown in FIG. 7, which consists of several spans, each having it's own cross-sectional properties, may be modelled as an equivalent system at the two extreme Nodes only, using static condensation. The resulting reduced stiffness matrix K' may be viewed as the equivalent beam stiffness matrix in terms of its end displacements and rotations, and similarly, the reduced load vector R' as the equivalent fixed end beam forces and moments of the applied load.
The static condensation method can be applied to condense any structural Model containing any number of Nodes. Although there is a lot of similarity between K' and k, there are two basic differences:
For a given "Finite Element" type, the order of k is fixed and predefined by the total number of degrees of freedom of the "Finite Element". On the other hand, the order of K' is variable and is equal to SN, where SN is the total number of independent degrees of freedom chosen.
The k matrix is automatically generated by the "Finite Element" solver used (either in close form or by numerical integration), whereas K' is obtained by static condensation. The similarly between k and K' suggests that K' may be viewed as the stiffness matrix of some Super Finite Element, which has no particular geometrical shape and whose Nodes are those designated as independent. This idea of a Super Finite Element has led to the more common name of "Super Element", and to the independent Nodes being called Super Nodes.
Once a solver is used to compute the independent displacement vector r', it is then possible to re-apply these displacements as boundary conditions to the Super Element Super Nodes and solve for the internal (i.e. dependent) displacements.
Finally, simple (or single-level) Super Elements are those consisting of the basic "Finite Elements" known to the solver, which is being used to perform the static condensation. Nested (or multi-level) Super Elements, however, may consist of some of the basic "Finite Elements", together with one or more other Super Elements at the time of static condensation. Usually, there is no limit to the number of nesting levels, and the only problem is keeping track of the data and matrices in the forward pass (i.e. static condensation) and the backward pass (recovery of Super Element internal results).
Turning to very particular structures, namely offshore platforms, we see that they must be structurally adequate for operational and environmental loading, practical to construct, and be cost effective. The selection of a configuration is based on functional requirements and methods of installation. This is especially true for structures situated in extreme water depths, such as the North Sea. Once the configuration has been selected by the design engineer, trial member sizes (e.g. tube diameter, thickness and length) must be assigned. These trial sizes are essentially educated guesses based on operational loads developed from equipment and materials layout, and estimated environmental loads. Estimates of the environmental loads are usually derived from experience with previous designs having similar environmental criteria. When assigning these trial sizes, consideration is given to the magnitude of the anticipated member forces, material used, local and overall member instability, overall buoyancy requirements, and hydrostatic considerations.
The horizontal and vertical forces exerted by wave action on individual members of the structure are calculated using the well known "Morison" equation, in conjunction with any of the available wave theories. These forces are functions of wave height, wave period, water depth and elevation above the mudline. In addition, the "Morison" equation includes empirical coefficients which depend on the size and shape of the member under consideration, and on the wave theory used.
In evaluating wave loads, the crest of the wave must be positioned relative to the structure, so that the loads have their maximum effect. Wind loads on the structure are developed using standard air flow theory. Sustained wind velocities are normally used for the computation of overall wind loads on the structure, but individual structural elements must be designed for instantaneous gusts.
If the structure is to be installed in very cold or seismically active regions, it may be subject to ice or earthquake loads, in which case more elaborate design and analysis procedures are used.
Once environmental loads are determined, they are combined with operational loads, and an estimate is made of the resulting pile mudline moments and axial forces. These approximate moments and forces are used in conjunction with foundation data to set trial values for pile penetration and make-up.
The design of major structural components of the superstructure and jacket is based on member forces determined in a 3-dimensional "Finite Element" analysis, which yields the resulting internal element forces, Node displacements and support reactions.
The pile analysis procedure employs a beam-column analysis using a finite difference technique to account for the non-linearity of lateral deflection of the pile and the natural variations in soil profiles along the length of the pile. The design penetration is based on the capacity of the soil to absorb the maximum design pile load with apropriate safety factors. Furthermore, to ensure that the pile can be driven to the design penetration without damage, pile driveability studies are performed for the available hammers.
Before the design solution of either the 3-dimensional "Finite Element" analysis of the superstructure and jacket, or the beam-column analysis of the piling can be considered finished, it is necessary to determine compatible conditions at the pilehead-structure interface. These equilibrium conditions are usually obtained using an interaction analysis procedure which yields the combined response of the linear structure and it's non-linear soil-pile foundation for any imposed static load condition.
The equilibrium conditions determined from the interaction analysis are now imposed on the structural Model in combination with appropriate design loads, and a static analysis is performed. The internal member forces determined in this analysis are employed to check the stress levels in the members. The stresses are compared to allowable stresses, as set forth in the design basis, and members are resized accordingly. Submerged members of the jacket must be checked for hoop stresses imposed by the hydrostatic head acting alone or in conjunction with axial stresses from the design cycle. If member resizing involves changes in outside diameter for a significant number of members, the overall waveload on the structure can be considerably different from that used to analyze the structure. In this case, the environmental loads must be determined based on the revised member sizes and the subsequent design steps must be performed again. The experienced structure designer can usually avoid this complication by the judicious assignment of trial member sizes. If the environmental loads are not significantly affected by the resizing of the structural members, the revised pile design can proceed using the boundary conditions from the interaction analysis. When dynamics do not become a consideration, this phase constitutes the final foundation design. However, deep water structures invariably require detailed assessment of response to dynamic loadings which necessitates further analysis of the foundation.
After the nominal sizes for main structural members have been finalized, it is necessary to design the connections of these members in accordance with the associated stress distribution. Geometric studies must be made to define joint layouts and to eliminate joints which might prove difficult to fabricate. At the intersection of tubular members, the chords or through members must be analyzed for punching shear stresses. Since the controlling stress levels at many of these joints are caused by loads which are cyclic in nature, due consideration must be given to high and low cycle fatigue. For some structures, the design of these joints may require special analysis to assess the cumulative fatigue damage, including consideration of dynamic amplification of stress levels for structures with significant dynamic response. Complex joints require detailed stress analysis to determine the appropriate stress concentration factors for use in a fatigue analysis and the correct distribution of loads. These joints are studid using "Finite Element" analysis.
Upon completion of the structural analysis and the sizing of the main members of the structure, the design of the deck and jacket detail steel begins and the final routing of piping, electrical, and instrumentation systems required on the structure can be completed. The design of these detail steel items and auxiliary systems are carefully coordinated with the layout of equipment and materials for drilling and production. Also, prior to designing the deck section, a lifting study must be carried out to ensure that the weight of the deck section with associated piping and equipment is within the lifting capacity of the derrick barge to be used on installation. To meet these criteria, the deck must often be fabricated in multiple sections and a lifting sequence is prescribed.
Once the jacket is fully designed, marine analysis can be performed for both towing and installation of the fabricated jacket. In the towing analysis, the stability and strength of the launch barge/jacket assembly is evaluated for environmental conditions due to wind, waves, and current expected to occur along the towing route. Forces caused by the barge response to these expected environmental conditions are used to design tiedown braces for fixing the jacket to the barge and to verify the structural integrity of the barge/jacket during tow. Towing analysis are also performed for the deck structure, piles, and any structure-related equipment that must be towed to the installation site.
When the barge is on location, the jacket is launched and then maneuvered from the horizontal free-floating position to a vertical orientation on the bottom. An installation analysis computes the forces on the barge and jacket during launch and simulates the behavior of the jacket from launch through upending.
Depending on the function of the offshore structure, pipelines may need to be installed for carrying the products to or from the structure. Analyses are performed for the design and installation of these pipelines and for the selection of associated laying equipment.
Small and medium size Finite Element Models usually present no real problems to the design of offshore platforms. It is only when dealing with large Models that the real difficulties, in using the Finite Element Method, are revealed. In general, these may be split into four categories: solver-related issues; data management issues; "Finite Element" modelling issues; and offshore engineering issues.
It is extremely difficult to select the most suitable "Finite Element" solver for a given problem, particularly when Users and/or Organizations have access to more than one solver. The suitability of a solver for a given problem is a matter of judgment and experience, and is usually related to: it's ease of use, it's cost of use, and on it's modelling and analysis capabilities.
Some solvers are user-friendly and easy to use, others are not. In any case, Users have to be proficient in the use of the solver used in order to avoid costly mistakes and erroneous results. Since it is not practical to expect Users to master the use of several solvers, more often than not, Users find themselves using inadequate solvers simply because they know how to use them. This usually results in Users being forced to make various modelling compromises and assumptions which may very well invalidate the analysis results. A good example here is the Multiple Point Constraints feature of the "NASTRAN" solver program used to mathematically define the dependency of certain degrees of freedom (DOF's) of one or more Nodes on the (DOF's) of other Nodes. Since some solvers do not support this basic modelling requirement, Users have to resort to various simulation techniques (e.g. by connecting these DOF's using dummy "Finite Elements" of infinite stiffness) to get around this problem. These dummy "Finite Elements", however, are very undesirable to have in the Model, particularly if the Model is to be used for Material Take-Off purposes.
Finally, once a solver has been selected, the modelling process and the Model data become totally dependent on that solver. This makes it virtually impossible to switch later to another solver, due to unforseen circumstances, such as system bugs or internal size limitations (e.g. exceeding the maximum number of Nodes or Load Cases). This is a very common problem which faces Users all the time, and the ability to switch over to another solver with minimal effort would be very advantageous.
Data Management Issues are related to the handling, management, and control of large amounts of data. Large Finite Element Models require strict human control and excessive human and computer resources. Mistakes are, therefore, very costly in terms of time and money. The preparation, storage, and control of the massive Model data are always error-prone. It is virtually impossible to maintain data consistency between individuals working on the same Model. It is extremely difficult to obtain accurate estimates of the computer resources required. For example, the CPU time needed to condense a Super Element is, amongst other things, dependent on the bandwidth. Unfortunately, this is not known until the Super Element has been scanned and/or processed by the solver. Inputting and modifying the Model data is usually done on a card-image basis rather than on a logical basis. For example, if a Node is to be deleted, it is usually up to the User to delete any additional data associated with that Node, such as: all the Elements connected to it and all it's applied loads; this process is very tedious and is certainly error-prone.
Finite Element Modelling problems are related to the lack of desirable modelling capabilities. It is virtually impossible to arrive at a near-optimum analytical Model (e.g. the best way to split a Model into Super Elements or the best Element or Node numbering scheme). The amount of work required to make a major modelling change is prohibitive. This discourage the User from making changes which are otherwise desirable. For example, the problem of splitting a Super Element into two or more smaller Super Elements involves tedious Node and Element renumbering operations. It is not always possible to perform various useful operations on the Model before it is ready for processig by a solver. For example, it is crucial that the incidences of certain "Finite Element" types are defined in a specific order (e.g. clockwise or anti-clockwise), otherwise, applied loads may be misinterpreted and may lead to erroneous results.
All the issues discussed so far apply to any large-scale Finite Element problem. Working in an offshore engineering design and construction environment, however, gives rise to even more problems.
The structural Models are usually very large, and hence, all the problems associated with large-scale Finite Element modelling apply. For example, although a global Model of an offshore structure may consist of a moderate number of BEAM Finite Elements, it may have to be analyzed under several hundred loading conditions representing different wave directions and characteristics. Typically the equivalent of some 100,000-200,000 card-images of distributed Finite Element loads could be stored in the database by one Application Program in one run unit (e.g. to conduct a fatigue analysis).
The structural analysis and design cycle requires the use of a large number of programs (e.g. pre-processors, solvers and post-processors), all of which operate on the same basic data. This raises the obvious need for a central file or database.
The structural design data is usually needed by several disciplines, all requiring concurrent access. This raises the need to support a multi-user online environment, with the necessary automatic recovery facilities.
Weather windows in hostile areas, such as the North Sea, usually mean extremely tight schedules. This raises the need for Project Managers to obtain progress reports reflecting the status of the design and analysis at any moment in time.
Structural modelling of offshore structures requires specific modelling capabilities which are unlikely to be supported by any of the general-purpose structural analysis systems (e.g. proper modelling of cutback values, insert piles, grouted piles and ungrouted piles).
It is very seldom that new offshore structures are ever designed from scratch. it is quite customary to use previously designed structures as a starting point. This raises the need to have intelligent access to historical data of previous structures.
It is important to have controlled archiving and restoring facilities in order to archive Models and restore them at a later date (this could be several months or years later, say, in order to do repair work). More important still, is that the archived database should include all information pertinent to the design codes wich were used for the initial design of the structure. For example, if a structure had been designed according to the 9th Edition of the API code, say several years ago, it may not pass today's more stringent 15th Edition code; hence the need to be able to reconstitute the entire design and analysis environment.
From the foregoing, it will be seen that there is a definite need for properly addressing the issues of engineering databases particularly for offshore platform design and appropriate database management systems (DBMSs). This engineering design requires more dynamic and more powerful DBMS's than usual.